Finite Group Databasebeta

← #11889146

Subgroups — #11889146

Order 1152.

964 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic
2#10594550C211yesmaximal, characteristic, complemented
3#10592461C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591480C211yesmaximal, characteristic, complemented
7#10591462C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590782C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#81383—31nomaximal
17#78762—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21#64149C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24#64096C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×#892C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63983—21no—
30#63977—21no—
31#63971—21no—
32#63909C2211yescharacteristic
33#63905—21no—
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36#63872C2211yescharacteristic, complemented
37#63867—21no—
38#63862—21no—
39#63857C2211yescharacteristic, complemented
40#63857C2211yescharacteristic, complemented
41#63855—21no—
42C2×#3716C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61D4×#67—31no—
62#5609—31no—
63#5529—31no—
64#5513—31no—
65C3×#482—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5114—31no—
69#5111—31no—
70#5042—31no—
71#5001—31no—
72#4967—31no—
73#4889—31no—
74#4882—31no—
75#4871—31no—
76#4864—31no—
77#4780—31no—
78#4779D311yescharacteristic, complemented
79#4776—31no—
80#4776—31no—
81#4770—31no—
82D3×#102D311yescharacteristic, complemented
83#4764—31no—
84#4764—31no—
85#4763—31no—
86#4762—31no—
87#4762—31no—
88#4762—61no—
89#4757—31no—
90#4731—31no—
91#4728—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107D3×#67—44no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625D411yescharacteristic
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3754—41no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744—41no—
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3716—22no—
144#3711—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—31no—
152C22×C3×C8—31no—
153C3×#121—31no—
154C3×#117—31no—
155C2×C3×C4⋊C4—31no—
156#953—61no—
157#940—31no—
158#940—31no—
159#940—61no—
160#939—61no—
161#938C2×D311yescharacteristic
162#937—61no—
163#937—61no—
164D4×Dic3—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—61no—
169#930—31no—
170#929—61no—
171C4×#67—31no—
172C4×#67—31no—
173#926—61no—
174#924—31no—
175#924—31no—
176C2×#208—31no—
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—31no—
180C2×#204—61no—
181C2×ΓL(1,𝔽25)—31no—
182C2×D3×C8C2×D311yescharacteristic, complemented
183#898—61no—
184#897—31no—
185#897—31no—
186#895—31no—
187#893—31no—
188#892C2×D311yescharacteristic, complemented
189D3×C4⋊C4C2×D311yescharacteristic, complemented
190#890—31no—
191#890—31no—
192#889—61no—
193#887—31no—
194#887—31no—
195#887—61no—
196#884—61no—
197#883—61no—
198#882—61no—
199#879—61no—
200#872—61no—
201#870—61no—
202C3×#107—31no—
203C3×#106—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic, complemented
210C3×#102C2×D311yescharacteristic, complemented
211C3×C22⋊C8—31no—
212#832—31no—
213#832C2×D311yescharacteristic, complemented
214#832C2×D311yescharacteristic, complemented
215#830—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8C2×D311yescharacteristic, complemented
221#817C2×D311yescharacteristic, complemented
222#816—31no—
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—61no—
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic
236#807—31no—
237#807—31no—
238#807C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255#638—81no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—42no—
277#626—42no—
278#626—42no—
279#625—22no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—31no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—31no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—31no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C2×#67—121no—
327C2×#67—124no—
328C22×Dic3—61no—
329D3×D4—22no—
330D3×D4—41no—
331D3×D4—62no—
332D3×D4—121no—
333D3×D4—124no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—62no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—121no—
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—61no—
365#217—21no—
366#217—31no—
367#217—31no—
368#217—61no—
369#217—61no—
370#217—61no—
371#214—62no—
372#214—121no—
373#214—121no—
374#214—122no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—21no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—121no—
407#208—121no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—62no—
414#204—121no—
415#204—121no—
416#204—122no—
417ΓL(1,𝔽25)—121no—
418D3×C8—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3AGL(1,ℤ/8)12yes—
436D32—84no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—31no—
456#127—91no—
457#126—181no—
458#125—91no—
459#125—181no—
460#123—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463#121—31no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—91no—
470C4×D4—91no—
471#117—31no—
472#117—181no—
473C2×C4⋊C4—31no—
474#107—31no—
475#107—91no—
476#106—31no—
477C4⋊C8—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102D3211yescharacteristic, complemented
488C22⋊C8—31no—
489C22⋊C8—91no—
490#97—91no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C22×D3—21no—
501C22×D3—42no—
502C22×D3—42no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—81no—
506C22×D3—121no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3D3×D411yescharacteristic
514C22×D3D3×D411yescharacteristic
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—61no—
523C3×D4—122no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—122no—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—42no—
543#67—62no—
544#67—62no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—242no—
550#67—241no—
551#67—241no—
552#67—242no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—121no—
565C2×Dic3—122no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568D12—21no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—121no—
574D12—121no—
575D12—122no—
576D12—122no—
577D12#23512yes—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—42no—
583C4×D3—122no—
584Dic6—62no—
585Dic6—61no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—121no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—121no—
600C2×C32—81no—
601C2×C32#54611yescharacteristic
602C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
603C2×C32#57711yescharacteristic
604C3⋊D3—81no—
605C3×D3—22no—
606C3×D3—41no—
607C3×D3—42no—
608C24—61no—
609C24—181no—
610C2×Q8—91no—
611C2×D4—31no—
612C2×D4—61no—
613C2×D4—62no—
614C2×D4—61no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—121no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—361no—
624C2×D4—364no—
625C2×D4C2×D3211yescharacteristic
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—61no—
629C22×C4—181no—
630SD16—182no—
631SD16—361no—
632SD16—361no—
633M16—361no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—91no—
637C2×C8—121no—
638C2×C8C2×D3211yescharacteristic
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4C2×D3211yescharacteristic
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—61no—
659C42—91no—
660C42—181no—
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—62no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—244no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—22no—
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—84no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—244no—
702C2×D3—244no—
703C2×D3#91112yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—81no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4C2×#23511yescharacteristic
715C3×C4#100411yescharacteristic
716C3×C4D3×#4111yescharacteristic
717C3×C4#100911yescharacteristic
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—41no—
723Dic3—62no—
724Dic3—61no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—121no—
729Dic3—122no—
730Dic3—121no—
731Dic3—121no—
732C32#331011yescharacteristic, complemented, Sylow
733C23—21no—
734C23—31no—
735C23—31no—
736C23—61no—
737C23—122no—
738C23—122no—
739C23—181no—
740C23—241no—
741C23—362no—
742C23—362no—
743C23—721no—
744Q8—181no—
745Q8—181no—
746D4—21no—
747D4—21no—
748D4—32no—
749D4—61no—
750D4—122no—
751D4—122no—
752D4—182no—
753D4—181no—
754D4—181no—
755D4—362no—
756D4—362no—
757D4—362no—
758D4—721no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—122no—
772C2×C4—181no—
773C2×C4—362no—
774C2×C4C22×D3211yescharacteristic
775C8—21no—
776C8—61no—
777C8—61no—
778C8—181no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—62no—
783C2×C3—81no—
784C2×C3—81no—
785C2×C3—121no—
786C2×C3—122no—
787C2×C3—161no—
788C2×C3#549011yescharacteristic
789C2×C3#565411yescharacteristic
790C2×C3C2×#91111yescharacteristic
791C2×C3#576211yescharacteristic
792C2×C3#577011yescharacteristic
793C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
794D3—22no—
795D3—42no—
796D3—41no—
797D3—241no—
798D3—241no—
799D3—481no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22—244no—
813C22—361no—
814C22—361no—
815C22—361no—
816C22—724no—
817C22D32×D411yescharacteristic
818C4—41no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—181no—
826C4—361no—
827C4D3×#23511yescharacteristic
828C4#6431411yescharacteristic
829C3—21no—
830C3#7876211yescharacteristic, complemented
831C3#8138311yescharacteristic, complemented
832C2—62no—
833C2—81no—
834C2—121no—
835C2—122no—
836C2—721no—
837C2#1059427211yescharacteristic
838C2D3×#91111yescharacteristic
839C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595288C2
hypercenter#102D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10594550C2semidirect
3. #10592461C2semidirect
4. C3×#4779C2semidirect
5. C3×D3×#102C2semidirect
6. #10591480C2semidirect
7. #10591462C2semidirect
8. #10591459C2semidirect
9. #10590946C2semidirect
10. #10590830C2semidirect
11. #10590782C2semidirect
12. #10590723C2semidirect
13. #10590592C2semidirect
14. #10590461C2semidirect
15. #10590422C2semidirect
22. C2×#3754C22semidirect
23. C2×#3744C22semidirect
24. #64096C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×#892C22semidirect
28. C3×D3×C4⋊C4C22semidirect
36. #63872C22semidirect
39. #63857C22semidirect
40. #63857C22semidirect
43. C2×#3711C22semidirect
44. C32×#102C22semidirect
45. #63641C22semidirect
46. #63636C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
78. #4779D3semidirect
82. D3×#102D3semidirect
182. C2×D3×C8C2×D3semidirect
188. #892C2×D3semidirect
189. D3×C4⋊C4C2×D3semidirect
209. C3×#102C2×D3semidirect
210. C3×#102C2×D3semidirect
213. #832C2×D3semidirect
214. #832C2×D3semidirect
220. (C2×D3)⋊C8C2×D3semidirect
221. #817C2×D3semidirect
238. #807C2×D3semidirect
487. #102D32semidirect
732. C32#3310semidirect
830. C3#78762semidirect
831. C3#81383semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105952882
#105945502
#105924612
C3×#47792
C3×D3×#1022
#105914802
#105914622
#105914592
#105909462
#105908302
#105907822
#105907232
#105905922
#105904612
#105904222
#813833
#787623